Border hopping to renew a tourist visa

Hi, I'll be moving to Argentina in about a month. I am currently reading some of the threads on here about immigration and visas and stuff. I am wondering, since I'll be teaching English, is it generally considered illegal and/or inadvisable to border hop to renew my visa as a tourist? Will this have long-term consequences such as not being able to gain citizenship or legal status? I am wondering if someone could link to some pertinent information about these topics or give me an answer. I am worried that the advice I got from the school I obtained my TEFL certificate from is wrong. They told me it's fine to border hop. But am I missing something here? Because it seems to me like if they deny my entry into the country after I border hop once or twice even, then I'd be screwed. Am I overthinking this or are there reasons why it'd be advisable to obtain some kind of longer-term work visa? I guess the information that has been omitted by the TEFL school is why schools that hire English teachers are not willing to sponsor work visas. I am wondering where to even start with all of this. And because my flight is in a month, I am more than a little worried about this. Thanks.

Sidenote: I was also considering just taking some classes on the side so that I could qualify as a student. I was wondering if this might be an option, too.